7.1 Introduction to Hypothesis Testing
• Key Concepts:
– Hypothesis Tests
– Type I and Type II Errors
– Probability Value (or P-value) of a Test
– Decision Rules
7.1 Introduction to Hypothesis Testing
• Consider the following scenario:
A fluorescent lamp manufacturer guarantees that the
mean life of a certain type of lamp is at least 10,000
hours. You want to test this guarantee. To do so,
you record the life of a random sample of 32
fluorescent lamps (see below). At α = 0.09, do you
have enough evidence to reject the manufacturer’s
claim? (#42 p. 376)
8,800
10,016
10,420
6,277
9,155
8,015
8,302
8,632
13,001
6,110
8,151
7,265
10,250
11,005
10,980
10,584
10,002
11,555
10,186
9,397
11,413
9,254
10,003
11,987
8,234
6,991
8,814
7,556
10,402
12,006
11,445
10,380
7.1 Introduction to Hypothesis Testing
• How can we test such claims?
– Start with a pair of statistical hypotheses or
statements about a population parameter.
• Null Hypothesis Ho
– Statistical hypothesis that contains a statement of
equality like ≤, =, or ≥.
• Alternative Hypothesis Ha
– The complement of the null hypothesis. It is a statement
that must be true of the null hypothesis if false.
• Practice forming Ho and Ha.
#12 p. 359
#16
7.1 Introduction to Hypothesis Testing
• When we conduct hypothesis tests, we always
work under the assumption that the null
hypothesis is true. We will reject Ho only when
there is enough evidence to do so.
– We need to be aware of two types of errors that may
occur in a study:
• A type I error occurs if a true null hypothesis is rejected.
• A type II error occurs if a false null hypothesis is not rejected.
– Practice Identifying Errors
#32 p. 360 (Flow Rate)
7.1 Introduction to Hypothesis Testing
• Definitions and Symbols we will need later:
– The probability of making a type I error is
known as the significance level of the test
and is denoted by α.
– The probability of making a type II error is
denoted by β.
7.1 Introduction to Hypothesis Testing
• Once we have identified Ho, Ha, and α, we need
to calculate the value of a test statistic and
then use it to make a decision about Ho.
– Once way to make that decision is to use the
probability value or P-value of the test.
P-value = the probability of obtaining a sample statistic with a
value as extreme as or more extreme than the one
determined from the sample data.
– The way we calculate the P-vale of a test depends on
the type of test we are working with (left-tailed, righttailed, or two-tailed). See page 354.
• Practice identifying the type of test
#38 p. 360 (Clocks)
#40 p. 360 (Lung Cancer)
7.1 Introduction to Hypothesis Testing
• How do we decide whether or not to reject
the null hypothesis?
– We use decision rules based on the P-value:
• If the P-value of the test is less than or equal to the
significance level, we reject Ho.
• If the P-value of the test is greater than the
significance level, we do not reject Ho.
Note: If we do not reject the null hypothesis, it doesn’t
mean we are saying Ho is true. We are saying we do not
have enough evidence to reject Ho.
#46 p. 361 (Gas Mileage)